The thermal relaxation time for a chemically non-equilibrated gluon plasma is calculated using the non-equilibrium Debye mass as the infrared regulator. The dependence of the thermal relaxation time on the fugacity is given. We find that there is a threshold fugacity λ g*. When λg < λ g*, τ NEQ/τ EQ decreases sharply with increasing fugacity, while λg > λg*, the ratio is almost unchanged.